Why is the Poynting Vector defined as E x B?

In summary, the Poynting Vector is defined as S = 1/u(E x B), where S points in the direction of the EM wave's motion. This means that for an EM wave moving from left to right, the electric field component always points up as the magnetic field component hits us in the face, and conversely, the electric field component always points down as the magnetic field components moves away from us into the page. The constant relative position of the B field to the E field was determined through experiments and is a necessary consequence of Maxwell's equations. The constraints added by Maxwell's equations also help to determine the relationship between the electric and magnetic fields in an EM wave.
  • #1
Usaf Moji
72
0
Poynting Vector is by definition:

S = 1/u(E x B), where S points in the direction of the EM wave's motion.

In other words, for an EM wave moving from left to right, the electric field component always points up as the magnetic field component hits us in the face, and conversely, the electric field component always points down as the magnetic field components moves away from us into the page.

My question is, how was this constant relative position of the B field to the E field determined, i.e. was it experimentally determined, or is it a necessary mathematical consequence of other formulae? In other words, why is it E x B instead of B x E? Is this just the way EM fields are measured to be, or is their some logical/mathematical reason for it?

All responses appreciated.
 
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  • #2
We know from Maxwell's equations in vacuum that the Laplacian(E) = UoEo*(d^2E/dt^2) and similarly for Laplacian(B) = UoEod^2B/dt.

These satisfy the wave equation. However, Maxwell's equations add constraints to the waves.

For instance, a wave traveling in the z driection Ez and Bz must equal zero to satisfy div(E) = div(B) = 0. (Waves are in a vacuum so div(E) = 0).

Also del X E also tells us that Bo = k/w(z X Eo) which is the relation you were discussing.
 
  • #3
Oh and sorry about the messy notation, I don't know LaTex.
 

1. What is the Poynting Vector?

The Poynting Vector is a mathematical representation of the flow of electromagnetic energy in a given space. It combines the electric and magnetic fields to show the direction and magnitude of energy flow.

2. How is the Poynting Vector calculated?

The Poynting Vector is calculated by taking the cross product of the electric field and the magnetic field at a specific point in space. It can also be calculated using the formula P = E x H, where P is the Poynting Vector, E is the electric field vector, and H is the magnetic field vector.

3. What are the units of the Poynting Vector?

The units of the Poynting Vector are watts per square meter (W/m^2). This represents the amount of energy flowing through a specific area in a given time.

4. What is the physical significance of the Poynting Vector?

The Poynting Vector is important because it shows the direction and rate of energy transfer in electromagnetic fields. It is often used to calculate energy flux, as well as to understand the behavior of electromagnetic waves and radiation.

5. How is the Poynting Vector used in practical applications?

The Poynting Vector has many practical applications, such as in the design of antennas, understanding the behavior of light in fiber optics, and calculating the energy output of solar panels. It is also used in electromagnetic radiation safety standards to ensure safe exposure levels to electromagnetic fields.

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